John, Paul, Jacques and Teddy

(Or, Cracking Lacan’s Formulae of Sexuation)

(from a correspondence)

…The most important thing is that I think I've found a way to understand Lacan's "formulae of sexuation."  I've been pondering this for weeks, and this is the first time I've attempted to set it down in writing.  I hope you'll bear with me.  I think I've found, not a way to understand Adorno through Lacan's formulae, but rather a way to decipher Lacan's formulae through Adorno.

On one afternoon in March of 1973, in a Paris lecture hall, possibly as I, a third-grader on the other side of the Atlantic, was seated in front of the TV watching the latest episode of "All in the Family," Jacques Lacan wrote four formulae on the blackboard that utilized symbols from symbolic logic, derived apparently from Frege:

The remarks he made on them were scanty.  He didn't even bother mentioning how they were to be read, though ostensibly they had something to do with "feminine jouissance" and the logic of the "not-all" - ideas he was busy developing that year.  People with an interest in Lacan have been puzzling over these things for three decades, as if they are the only surviving clues to some lost ancient language.  Somehow everybody managed to figure out that they were supposed to be read as follows:

1.  There is at least one x which is not submitted to the phallic function.

2.  For all x, the phallic function is valid.

3.  There is not one x which is not submitted to the phallic function.

4.  For not all x, the phallic function is valid.

Lacan said that the first two formulae (which he drew on the left of the blackboard) were "masculine," whereas the last two (which he drew on the right) were "feminine."  Most interpreters have inferred that they may be read in more clearly Freudian terms in this way:

1.  There is at least one man who is not castrated.

2.  All men are castrated.

3.  There is not one woman who is not castrated.

4.  Not all women are castrated.

How is this usually understood?  It's necessary to begin with Freud's myth of the primal father.  We begin with the second formula.  "All men are castrated."  Why are they castrated?  Because they submit to castration at the hands of the primal father, who is the one who in the first formula is not castrated and thus gets to enjoy all the women of the primal horde.  Then we move to the fourth formula.  Why are women not castrated?  Because they don't bear an organ that can be castrated.  Yet why is there not one woman who is not castrated (formula three)?  Because, in a sense, women are already castrated, if we take castration to mean simply "not having an organ."

Of course it gets much more complicated when we consider that by "castration" we are to understand "symbolic" rather than "real" castration.  But we don't need to get into the nitty gritty of Lacan's complicated interpretation of Freud on castration to follow my argument as to how they should be read, which goes something like this:

Let's begin with Adorno.  One of the central themes of Adorno's essay on "Music, Language, and Composition" is the question as to the respect in which music may be considered a language.  Subordinate to this is the question as to what "signification" means, assuming that languages are signifying systems and that music is or may be classed as a signifying system.  There is a logic that runs through the essay that can be stated in terms of Lacan's formulae as follows (I'll state them in a 2-1-4-3 order so that the logic is easier to follow):

1.  All languages are systems that signify.

2.  There is at least one language that does not signify.

3.  Not all languages signify.

4.  There is no language that does not signify.

In the first formula it is stated that all languages signify - i.e. use signs to point to things outside of language.  In the second formula, it becomes apparent that there is (at least) one language that does not meet this criterion - i.e. that in some way does not (or does not fully) signify.  That language is music.  The signs of music (or "musical symbols," as Adorno prefers) do not allow us as do other languages to point in a clearly discernible way to things outside of language.  The third formula seems similar to the second but is less specific.  It simply suggests that there are some languages that do not meet the criterion stipulated by the first formula.  The fourth formula, however, suddenly announces that there is no language that does not meet the first formula's criterion - thereby excluding music from the privilege of being a signifying system that does not clearly and discernibly point to things outside of that system.

How are we supposed to understand all of these apparent contradictions?  The key is that between the second and third formulae a couple of things happen.  First, there is a shift in the concept expressed by the predicate.  In the first two formulae, the predicate "to signify" means "to allow access to meanings outside of language."  Language consists of signifiers that point to clearly discernible signifieds or referents outside of language.  In the second two formulae, however, "to signify" means "to pass from one signifier to another."  There is no signified meaning, no objectal world outside of the signifiers that constitute language.  

Thus we can now read the formulae as follows:

1.  All languages allow access to meanings beyond language.

2.  There is at least one language (music), however, that does not allow access to such meanings.

3.  Not all languages a) allow access to meanings beyond language [or] b) are sets of signs that do no more than refer to each other.

4.  There is no language that is not a set of signs (or signifiers) that do no more than refer to each other.

The third formula has to be read with the possibility of alternative meanings of the predicate (3a and 3b), as it does not become clear until the fourth formula that the state of predication has indeed changed.  On an initial reading of the third formula, it seems that we are merely restating what has been stated in the second formula - namely, that music is an example of a language that does not allow access to an ultimate signified or meaning.  However, after reading the fourth formula, with the change in predication that has taken place, it becomes apparent that the third formula refers, not to music, but rather to all of those languages that unlike music are more than sets of signs referring merely to each other and that DO allow access to meaning beyond language.  

To restate this all in simple terms, Adorno is saying that music is a language, but a sort of language that does not allow access to clearly discernible referents/signifieds/meanings.  A simple statement, maybe - though according to the logical formulae I have discerned at work in the essay, one that is arrived at through a rather tricky set of maneuvers. 

This, however, is not the end of it.  Not only has the predicate undergone an alteration, so has the subject.  After the second pair of formulae, language is no longer a set of signs that refers to things outside of itself; it is instead a set of signs that ultimately refer to each other.  This alternate conception of language, I believe, is the sort of language that Lacan referred to as "lalangue," which Bruce Fink has translated as "llanguage."  In Adornian terms, languages such as music that do not ultimately point to things beyond them are "llanguages."  So what we must finally accomplish is a sort of synthesis posed to the thesis presented in the "masculine" formulae and the antithesis of the "feminine" formula, which is simply a restatement of the fourth formula with the newly produced subject and reads:

"There is no llanguage that is not a set of signs that do no more than refer to each other."

Yet this newly created "llanguage" must be understood, in fact, to include not only the initial "llanguage" (music, in this case) but in addition all of the other entities that we formerly termed "language."  In other words, all language is ultimately "llanguage" and is unconcerned in the end with things outside of the set of signifiers of which they are comprised.  

And we can locate this very specifically in Adorno's text.  He has told us, in accordance with the "masculine" logic of the first two formulae, that language in general grants access to meanings outside of language but that specifically musical language does not.  However, at one point he says that the meanings in which language unfolds are meanings that ultimately refer merely to each other - which is as much as saying that language is an endless movement from signifier to signifier with no resting points in signifieds that "mean."

What's the point of all this?  What, I believe, Lacan was trying to get at is that whenever in discourse there is a certain systematization of argumentation that implies universality, the entire apparatus is founded on an exception; this exception is simultaneously a secret trap-door which opens up onto an inverted, "feminine" universe.  I believe (and hope to show) that Adorno's particular formulation of dialectical method produces such universalities-founded-on-exceptions on an almost page-by-page basis.

Let's return to the standard reading of the original formulae (again, inverting the original order in which they're stated in order to better grasp the logic).  Thus:

1.  There is at least one man who is not castrated.

2.  All men are castrated.

3.  There is not one woman who is not castrated.

4.  Not all women are castrated.

I believe, however, that this is not exactly what Lacan intended.  In fact, the four formulae, I believe, are meant to be read (initially) as follows:

1.  There is at least one man who is not castrated.

2.  All men are castrated.

3.  There is not one man who is not castrated.

4.  Not all men are castrated.

Let's put to the side the complicated shift in predication (i.e. the shift in what is indicated by the concept "to be castrated").  Let's examine instead what happens with the subject.  What happens in the second pair of formulae is that "man" as a genus has, in Hegelianese, undergone a "diremption" into the species "man" and "woman," similar to what happened with the diremption of language into language and "llanguage" above.  That is what allows us to substitute, in formula 4, "woman" for "man" as we did above (i.e. "llanguage" for "language").  When we accomplish this, however, "woman" is now inclusive of "man" - the order of species "woman" under the genus "man" has been inverted...only, we cannot say "genus woman, species man," as that would be partaking of the universalist logic native to the "masculine" formulae of the first couplet.

This logic of what I'll call "inversion through exception" can be illustrated a propos of certain passages of Adorno on popular music.  For instance:

1.  All popular music is administered.

2.  There is at least one (sort of) popular music that is not administered.

3.  Not all popular music is administered.

4.  There is no popular music which is not administered.

The first formula is self-explanatory.  The second refers to those near-exceptions that Adorno rarely and as if grudgingly makes.  The problem is he doesn't mention any names, as he does with film (Chaplin, Welles...).  Well, let's give him a bit more rope than he probably deserves and name someone - say, Charlie Parker, as he seems to meet all the criteria that Adorno occasionally proposes.  Next comes the third formula with its seeming repetition of the second.  Finally, the fourth, a seeming replication of the first.  But the fourth formula, now that we know that at least Charlie Parker is not administered...how can we square it with formulae 2 and 3?  It works because the predication has changed.  "Administered" now means "self-administered," or "mediated" in Adornoese.  Yes, Charlie Parker's music is just as much part of the "administered world" as is that of Paul Whiteman - the difference is that, in Charlie Parker, the administration is no longer "from above" but rather "from within."  

But here we get to the tricky part: In each of our examples above (the original example from Lacan and the example apropos of music and language), the formulae produced two new objects that were not given in the judgment of the first formula.  In Lacan's example, the primal father who is not castrated and thus gets to enjoy the women of the horde is the exception that comes to light in formula two, and woman is the sub-species of man produced through diremption in the second couplet.  In the example from "Music, Language, and Composition," music is the exception, "llanguage" the dirempted sub-species of language.  We have named for Adorno the exception in our final example (the music of Charlie Parker).  But what is the sub-species of "popular music" produced through the "diremption" of the second couplet?  Answer: "serious music."  Or, as Adorno says condescendingly, "good bad music."  So we must accomplish the final turn with the dirempted element and say: "There is no serious music which is not administered."  And now the concept "serious music" includes all music, even popular music.  

No, Adorno didn't say that...But the logic is there.  You have a universality founded on an exception.  All it takes is formulae 3 and 4 to produce the rest.  And also to suggest why Adorno is in a way so undialectical in his thought on popular music.  He could indeed state that there was an exception, but he couldn't bring himself to dignify it with a proper name.  

(An aside: Note that the exception and the dirempted element always form a pair: Primal father/woman; music/llanguage; Charlie Parker/serious music.  This must at least in part explain why the happiest reigns in monarchies since the time of Hobbes or earlier have been when a woman has held the throne (Elizabeth, Catherine...).  When such an occurrence takes place, we have a coincidence between the exception (monarch as a trope for the primal father) and the sub-species of the universal genus (woman) that has come to permeate the medium in which the (masculine) universal draws its sustenance and proves itself far from universal from the point of view of someone who has stuck his or her nose through the black hole of the exception.)

These formulae which I believe I have at long last cracked (as we approach the 30th anniversary of the day when Lacan plastered them up on a board in front of the bewildered Parisian intelligentsia) can be used to explain a whole slew of things regarding music.  Wherever there are hints of conceptual systematization there must also be an exception.  And where you have a system founded on an exception, you have a "Lacanian order of sexuation."  Take a look at this, for instance:

1.  All chords are subordinate to the tonic.

2.  There is at least one chord that is not subordinate to the tonic (you guessed it – the tonic itself).

3.  Not all chords are subordinate to the tonic.

4.  There are no chords that are not subordinate to the tonic.

You might call these the "four fundamental laws of tonality."  In the second couplet, the tonic "dirempts" itself into the "empirical tonic" of the first couplet (i.e. C major, or whatever particular key we have before us) and the "tonic function."  If the empirical Queen Elizabeth of England is merely the current "placeholder" of the English monarchy, the empirical A-flat major of Beethoven's Op. 110 piano sonata is merely the "placeholder" of the tonic.  The difference between this last example and the examples given above is that the exception brought to light in the second formula (the "empirical" tonic, understood as the particular key currently serving as tonic) and the new element brought about through diremption in the second pair of formulae (all other chords insofar as they could potentially usurp the tonic function) are identical to a large extent.  The identification of the exception with the dirempted element (a version of the Hegelian concept of speculative identity?) is thus possible in systematic logic and may help to explain why tonality has held together as a system for so many centuries.

But isn't this all just a lot of logical rigmarole that merely seeks to explain an empirical reality with a convoluted set of epicicular rules?  

The other day a 5th-grade kid I teach privately approached me and told me that she had been chosen as her elementary school class' representative in this year's English song competition and that she needed me to help her choose and prepare a song.  "How much time do we have," I asked.  "Three days."  "Jeez, why didn't you tell me a month ago?"  "I forgot."  The only thing I could come up with on such short notice that was interesting and simple enough to teach a non-native learner of English was the Beatles' "Hello Goodbye."  So we sat down with the Magical Mystery Tour CD, she learned the song in a manner of minutes, laughing at the goofy picture of a doubtlessly drugged-out Fab Four dressed up in the idiotic costumes that adorned that production, and easily learned the simple, amusing actions I've used for years at the kindergarten to teach this song.  The day before the competition she says to me, "My teacher says I can't use any recordings which have singing on them."  "Great...well then you'll have to do it a capella."  "What's that?"  "It means sing by yourself without the music."  We practiced, and she couldn't keep the tune without the CD playing along in the background.  So I said, "OK, let's go to the piano and I'll try to make a recording for you.  After 30 anxiety-filled minutes I had come up with a pretty good piano accompaniment with a right-hand melody and standard Alberti-bass left-hand accompaniment.  Not that tricky - sort of a loop structure as with the Bowie song "Golden Years" I analyzed awhile back, though much simpler, with only three chords, I, V and VI.  I recorded it in C major.  I stumbled across one very interesting thing as I was doing so.  You know the part of the melody that goes with, "I don't know why you say good-bye, I say hello."  This is a cadential thing.  The melody goes G-C-E-F-F-E-D-C-C-B-B-C.  The accompaniment (played in the octave range around middle C): V(6-4)-V(5-3)-I (G-E-C-E/G-D-B-D).  BUT...Your first impulse after playing the cadential figure on G is to either jump up to middle C or descend to the one below it for a root-position tonic triad to accompany the C on the "o" in "hello."  What I immediately found was that it produced an awful, tawdry, "inauthentic" sound that wasn't at all what Paul McCartney came up with on the recording (and which had nothing to do with the parallel 5ths that can easily be avoided through proper voice-leading, assuming that the old prohibition against parallel intervals still matters within the Beatles' harmonic universe).  The correct thing to do is to keep playing in the second inversion (G-E-C-E).  And that's the great secret of this simple but compelling song - you never have a root position sounding of the tonic, although you always know precisely what key you're in...the whole thing just keeps humming along in a loop anchored on the G shared by the tonic and the dominant.

What McCartney has done (unknowingly, of course) is illustrate one of the key laws of tonal harmony...that the "empirical tonic" can "dirempt" itself into its various empirical manifestations on the one hand and its function qua tonic on the other and can eliminate that manifestation (the root-position) that most clearly coincides with the tonic function without permanently damaging its integrity qua tonic.

You could even use this to play John off against Paul and vice versa.  Although both Lennon and McCartney are popularly viewed as the greatest songwriters of their generation, hasn't it been true at least since John's death that John is sort of given the edge, even though no one wants to come out and say directly, "Yeah, Lennon was the greater of the two"?  Yet I believe that the two of them could be analyzed in terms of the masculine/feminine dichotomy implicit in Lacan's formulae.  Doesn't John always take the form of an exception?  "Yeah, pop music is mostly crap...But occasionally you get one guy with real insight...John Lennon for instance."  On the other hand, isn't it commonly acknowledged that Paul sort of remains more closely within the confines of pop music's general crappiness...just that he's more refined?  But I think that once you accomplish the feat of sticking your nose through John's exception and looking "inside-out" at Paul, you find that, precisely because Paul renounced the logic of the exception, he more completely exhibits the real greatness and the real genius of pop music in all its fullness.  This could be illustrated in a variety of ways.  Take their Christmas songs penned during the '70's.  First you have John and Yoko's "And so this is Christmas" (what's the real title..."Happy Christmas, the War is Over").  It's a great song, showcasing John's "exceptionalism" - you have the odd exception of his allowing his Japanese-accented wife to sing a verse of a song that will become a big hit, you have hints at modulation in the pick-up to the chorus, with its accentuation of the sub-dominant, you have the attempt at writing a "profound," "socially meaningful" lyric (whereas Paul as a lyricist is clearly better when he accompanies his terse statements in musical logic with dumb-ass nonsense as in "Hello Goodbye"), then you have the "Hare Krishna" chants at the end (doesn't it show Paul's comparative sobriety that he abandoned the hokey forays on the part of the Fab Four into pop versions of "Eastern wisdom" several years earlier than John and George?).  A few years later, Paul takes the incipit melody from John's song (5-1-2-3) and pens the urbane, Stevie Wonderish "We're Just Having a Wonderful Xmas Time."  No exceptions here...just Paul's exquisite utilization of a few key elements, and the wonderful addition in the middle that really makes it the great song it is of a "ding-dong-ding-dong" choir sung by his fellow Wings members with clear allusions to 19th-century English Xmas carol harmonies.  You'd be hard pressed to decide which is the better song.

What do we learn about pop music through such an employment of Lacanian logic?  We learn that the great merit of 20th-century popular music has been to whittle away at the excesses that have accumulated like unwanted ballast on the basic logical configurations that have structured Western musical thought at least since the late Renaissance.  In a way, popular music's logic is far more rigorous (better said: it has the potential for greater logical rigor) than "serious" music because the logic has been reduced to its barest essentials.  I was in a music store recently, contemplating the seventeen volumes that Schumann's piano works print out to, thinking, "How is it possible for one man to have written so much piano music in a relatively short life-span?"  Yet how much of it is still performed today?  And why, in contrast to the piano music of Beethoven or Brahms, such a small percentage?  The answer must lie beyond the simple laws of distribution and consumption that Adorno might point to.  I'll bet that at the core of these hundreds of little pieces that are never heard today you have structures very similar to those of "Golden Years" or "Hello Goodbye."  Yet how much of a greater percentage of McCartney's songs will still be hummed 100 years from now (assuming that we haven't blasted Mother Earth to bits by then, which is entirely possible)?  Isn't it in a way so much harder to write a "really good pop song" than it is to write a complicated 19th-century piano sonata, because one is dealing with a tonality that has been laid bare?  (Just as all the Cantos of Ezra Pound or Eliot's wordy Waste Land are worth nothing against the 128 syllables of Frost's "Stopping by Woods on a Snowy Evening" or Dickinson's "I Had Not Minded Walls.")  And what an achievement to have written several dozen or more "really good songs," when all that we remember of Schumann's solo piano works is Carnival, Papillons, Kinderszenen, "Vogel als Prophet," and a few others.

(Of course all of this is heavily exaggerated for argument's sake.  If really pressed, of course I wouldn't say that "Paul McCartney is a greater musical artist than Robert Schumann" - though I might be tempted to place Bob Dylan and David Bowie in Schumann's rank…)